Kinetic NMR Experiments

Analysis based on time-resolved NMR measurements was applied for kinetic studies.

During these experiments the reaction cannot be stirred within the NMR tube. The reactants can move only via diffusion. The experiments were performed in toluene-d8for best comparability of the results with non NMR experiments in the conventional solvent.

The process found is leading to several species which could be clearly characterized. The assignments to formed species are shown in Figure 4.4. The measurement data at the Zr:Mg ratio 1:20 was provided by Adrian Deinert within his bachelor thesis.

1.54

Cp*2ZrBzClMgBz2

Cp*2ZrBz2MgBz2

BzMgBz

Cp*2ZrBzClMgBz2

C B

Figure 4.4: Determined species via time-resolved NMR measurement of monomer-free CCG model system using Cp*₂ZrCl₂ (A) and BzMgBz at 80^◦C, c(Cp*₂ZrCl₂) = 4.6 mmol L⁻¹ c(BzMgBz) = 44 mmol L⁻¹in toluene-d₈with only every tenth measurement shown for clarity reasons (yellow - short reaction time, green - long reaction time).

The catalyst precursor (Cp^*2ZrCl2,A) has the signal at 1.85 ppm which is rapidly trans-ferred into an aduct ofAand BzMgBz (Cp^*2ZrCl2MgBz2,B) yielding a splitted signals at 1.89 ppm and 1.87 ppm. It is considered as a bimetallic Zr-Mg-complex with the chloride atoms as bridge atoms. The splitting may be caused by the presence of two or more kinds of magnesium clusters.^[267] With increasing time a signal at 1.98 ppm (Cp^*2ZrBz(Cl), C) appears and is nearly stable during measurement. It is shifted strongly to lower field compared to AandB. It is assumed that it belongs to a

beny-zlated complex in which the chloride is not directly or weakly coordinated to the zirco-nium. It yields a positively charged catalyst because the BzMgBz acts as an activator.

This is in agreement with literature data from complexes of [Cp^*2ZrR]⁺cations.[91,270,271]

Two new signals emerge at 1.77 ppm and 1.75 ppm which correspond to the bridged mono-benzylated complex (Cp^*2ZrBzClMgBz2,D) and their combined integrals increase similarly to the signal at 1.55 ppm. This signal is the benzyl moiety bridged between zirconium and magnesium (Cp^*2ZrBzClMgBz2,D). At higher reaction times the signals of the bridged di-benzylated complex appear at 1.70 ppm (Cp^*2ZrBz2MgBz2,F) for the ligand and at 1.56 ppm for the benzyl groups Cp^*2ZrBz2MgBz2,F). The signals for the bridged mono- and di-benzylated complex are in agreement with literature^[272]for the ligand signals while the bridged benzyl moieties are slightly shifted to higher field. At 1.62 ppm a signal similar to the benzyl moieties of the unbridged and fully alkylated complex (Cp^*2ZrBz2,E) are found while the ligand signals were not observed due to the low concentration.^[272,273]The signal of dibenzyl magnesium (BzMgBz) is found as a broad peak at 1.66 ppm^[274]which shifts slightly to lower field with increasing reaction time. In Figure 4.5 this effect could be shown via a plot of the peak maximum against reaction time.

0 5000 10000 15000 20000 25000 30000 35000 40000 1.645

1.650 1.655 1.660 1.665 1.670

BzMgBz /ppm

t / s

Figure 4.5:Alteration of the chemical shift of BzMgBz in monomer-free CCG activation at 80^◦C.

In comparison with the formation ofBandD(see Figure 4.7 on page 45) the signal shift is correlated to the proceeding reaction. The small part of BzMgBz in the coordination sphere of the complexes is exchanged by molecules from solution. While the peaks are not broadened, the observation shows that the reaction is faster than the time scale of

the NMR-experiment.

For the determination of concentrations the signals were integrated and the NMR raw data was normalized with the solvent signals of toluene. The exact procedure is de-scribed in the experimental section (see experimental part 9.1.5 on page 197). One example of the measurements is shown in Figure 4.6 on the next page. Beginning from the catalyst precursor AcomplexBwas formed rapidly and the concentration of Ais detectable for around 2 500 s. With proceeding reaction time complexBis transferred slowly into complexD and complex Fand both signals occur at the same time. The formation of C is detectable shortly afterwards with an almost stable concentration during the measurement. It is assumed that this complex is the catalytic active species for polymerization. The concentration of BzMgBz is measured simultaneously and the consumption is in direct correlation to formation ofDwhile the formation of complexF is overlaid by side effects (see Figure 4.7 on page 45).

BzMgBz

kalkyl2 - BzMgCl

Scheme 4.3:Kinetic Scheme of the process of monomer free CCG activation outgoing from complex Aby BzMgBz via the formation of complexCandD^P0and further reaction to complexF^P0. Complex Cis assumed to be catalytic active. The suffix P states the amount of polymer chains present in the complex, in this case x = 0.

The combination of these results leads to the kinetic Scheme 4.3 for monomer-free cata-lyst activation in CCG. In the beginning, the catacata-lyst precursorAis in equilibrium with species B^P0 (The suffix P stands for the amount of polymer chain present in the com-plex, here x = 0) via reversible association and dissociation of BzMgBz. Outgoing from speciesB^P0a second reaction pathway leads to speciesCby intramolecular alkyl-chloride exchange followed by dissociation of a Grignard reactant. Via reversible association and dissociation of BzMgBz speciesCis in equilibrium with speciesD^P0. By a second intramolecular alkyl-chloride exchange at complexD^P0 and dissociation complexE^P0

0 5000 10000 15000 20000 25000 30000 35000 40000 0.000

0.001 0.002 0.003 0.004 0.005 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

F

C B

A

F B

D Cp*

2 ZrCl

2

(A) Cp*

2

ZrBzClMgBz 2

(D) Cp*

2 ZrBz

2 MgBz

2 (F)

Cp*

2 ZrCl

2 MgBz

2

(B) Cp*

2 BzCl (C)

[A;B

P0 ;C P0 ;D P0 ;F P0 ]/molL

1

t / s

Figure 4.6:Concentration vs. time profiles of the different complex species for monomer-free CCG activation at 80^◦C withc(Cp*₂ZrCl₂) = 4.6 mmol l⁻¹c(BzMgBz) = 44 mmol l⁻¹in toluene-d8.

0 5000 10000 15000 20000 25000 30000 35000 40000

Figure 4.7:Comparsion of concentration time profiles of complexDandFwith BzMgBz measured at 80^◦C in toluene-d8.

and a further Grignard reactant are formed. SpeciesEis in equilibrium with speciesF^P0 by association and dissociation of BzMgBz which is found as the final product of the reaction processes in NMR.

For further investigations of the kinetics the different reaction rate equations were de-scribed by classical reaction time laws (see eq. 4.1 to 4.6).

d[A]

Due to the complex assembly of equilibria and following reactions an analytical solution was not possible. Thus numerical methods were the ones of choice. The program

package PREDICI^TM was chosen to allow an easy transfer of the results to a model system containing polymer information (see section 2.4.4 on page 34 for more details to this program package). For simulation with PREDICI^TM a kinetic model has to be declared. In the following the input reactions in PREDICI^TMnomenclature are present:

A+BzMgBz ^kex0 B^P0 (4.7) B^{P0 kact0} A+BzMgBz (4.8)

B^{P0 kalkyl1} C+BzMgCl (4.9)

C+BzMgBz ^kex1 D^P0 (4.10) D^{P0 kact1} C+BzMgBz (4.11)

D^{P0 kalkyl2} E^P0+BzMgCl (4.12)

E^P0+BzMgBz ^kex2 F^P0 (4.13) F^{P0 kact2} E^P0+BzMgBz (4.14) BzMgCl+BzMgCl ^kschlenk BzMgBz+ClMgCl (4.15) In all cases simple “elemental” reaction steps were applied and the reaction 4.15 of benzyl magnesium chloride was additionally declared because during the reaction a white solid precipitates which is magnesium chloride. The formation of dibenzyl magnesium is yielded by the Schlenk equilibrium of two Grignard species formed during reaction 4.9 and 4.12. The reaction is quantitatively due to the participation of MgCl2.

The NMR measurements allowed the time dependent concentration determination of six from the seven occurring species. With this comprehensive kinetic data the rate coefficients are available and can be estimated by modeling on the basis of the model scheme. The results of the parameter estimation tool of PREDICI^TMare shown in Table 4.1.

In Figure 4.8 the simulated time evolution of the species concentrations by PREDICI^TM parameter estimation are shown together with the experimental data. The resulting fits are in agreement with experimental data and point towards the validity of the mechanistic scheme as well as for the reliability of the estimated kinetic coefficients.

Whilekalykl1andkalykl1were estimated independently the values ofkexandkactdepend on each other. Thus, determination of individual values is impossible. Simulation for different reaction rates with constant ratio indicated no influence on the concentration profiles for the applied variety. Therefore the values of kact were fixed to the value

Table 4.1Parameters estimated by PREDCI of momomer free CCG activation modeling at 80^◦C, c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹,c(BzMgBz) = 0.044 mol L⁻¹in toluene-d₈with fixedkactvalues at 1 s⁻¹.

coefficient value unit

kex0 972 L mol⁻¹s⁻¹ kex1 19808 L mol⁻¹s⁻¹ kex2 7994 L mol⁻¹s⁻¹ kalkyl1 1.21 10⁻³ s⁻¹ kalkyl2 6.96 10⁻⁶ s⁻¹ kSchlenk 1000 L mol⁻¹s⁻¹

0 10000 20000 30000 40000

0.000 0.002 0.004

0 10000 20000 30000 40000

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014

0 10000 20000 30000 40000

0.000 0.005 0.010 0.015 0.020

0 10000 20000 30000 40000

0.032 0.034 0.036 0.038 0.040 0.042 0.044

[B];[D]/molL

1

t / s D

B

[F]/molL

1

t / s

[C]/mmolL

1

t / s

Simulation

Experimental

[BzMgBz]/molL

1

t / s

Figure 4.8:Simulatied and experimental concentration vs. time profiles with the input data of Table 4.1.

of 1 s⁻¹ for PREDICI^TM simulation describing the ratio as an equilibrium constant by modelingkex. Within the variety the reaction rates are only dependent on the applied ratio. The exact values are of importance in presence of monomer (see Chapter 5.1.3 on page 111). The reaction rate coefficient for the Schlenk equilibrium was chosen fast to represent the participation process of MgCl2while regeneration of BzMgBz. The value of 1 000 L mol⁻¹s⁻¹is not considered of high significance.

Based on these results the mechanistic scheme and the simulation results were reviewed for simplifications and optimization of the determination of kinetic coefficients. The PREDICI^TMparameter optimization tool was found not to be the optimal method to gain the best suitable kinetic data for the chosen scheme. The data of Table 4.1 indicates that the association/dissociation processes are faster by several orders of magnitude than the ligand exchange (alkylation) reactions and it can be considered thatAandB^P0 as well asCandD^P0are in equilibrium in the relevant time scale for the ligand exchange. This allows that equation 4.1 may be rewritten to define the equilibrium constantKZr,1(see eq.

4.16).

k_ex0 k_act0 =

B^P0

[A] [BzMgBz] =K_Zr,1 (4.16) To verify this approximation equation 4.16 was applied to the simulation data (see Figure 4.9a)upper part). After fast establishment of equilibrium the concentration ratio of

B^P0

/[A] [BzMgBz] has a constant value equivalent to the input ratio kex0/kact0. A slight influence of the simulation process is found while the process is independent from the ligand exchange reaction. This situation can be transferred simultaneously to the reaction ofCwith BzMgBz toD^P0 (Equation 4.9) and it is characterized by the equilibrium constantKZr,2(see Equation

k_ex1 k_act1 =

D^P0

[C] [BzMgBz] =K_Zr,2 (4.17) The calculated ratio of kex1/kact1 from the species concentrations ratio D^P0

/[C] [BzMgBz]reaches fast an equilibrium value (see Figure 4.9a)lower part). To further validate these approximations it was cross-checked with the experimental NMR-data. The determined concentration ratios of

B^P0

/[A] [BzMgBz] and D^P0

/[C] [BzMgBz] are shown in Figure 4.9 b). The results support the approxima-tion and the kinetics can be simplified by the applicaapproxima-tion of equilibrium reacapproxima-tions ofA andCwith BzMgBz and the description with the equilibrium constantsK1,ZrandK2,Zr. The equilibrium reaction ofAwith BzMgBz (Equation 4.16) can be inserted into equation

0 1000 2000 3000

0 10000 20000 30000 40000

19800

0 10000 20000 30000 40000

4000

0 500 1000 1500 2000 2500 3000

1100

Figure 4.9:Simulated (a)) and experimental (b)) results for determination ofK_Zr,1with equation 4.16 andK_Zr,2with equation 4.17 with the input data of Table 4.1 for monomer-free CCG activation. The red lines show the constant ratio of concentrations.

4.2. The reaction order is simplified to a pseudo-first-order reaction with respect to the concentration ofB^P0 only reduced by the alkylation reaction (see Equation 4.18).

d B^P0

dt =−k_alkyl1 B^P0

(4.18) And for the reaction ofCwith BzMgBz equation 4.17 is inserted into equation 4.4 giving a pseudo first-order reaction for the consumption ofD^P0by the alkylation reaction (see Equation 4.19). Both equations are cross-checked with first-order reaction plots for the concentrations of B^P0 andD^P0 (see Figure 4.10,a)). In both cases it can be seen that a nearby perfect linear fit is achieved. It supports the validity of the approximations discussed previously.

In comparison with the input data of simulation the determined rate coefficientskalkyl1 = 1.17×10⁻³s⁻¹ andkalkyl2 = 6.88×10⁻⁶s⁻¹deduced from the slopes of the linear plots are ca. 3 % smaller. This is in agreement with the confidence interval of the estimated data.

It can be concluded that the approximations found by simulation allow the simple de-duction ofkalkyl1andkalkyl2via first-order plots of the experimental concentration profiles of speciesB^P0andD^P0and ofKZr,1andKZr,2calculated with experimental concentrations

0 2000 4000 6000 8000 10000 0

3 6 9 12

0 10000 20000 30000 40000

0.0 0.1 0.2

0 10000 20000 30000 40000

0.0 0.1 0.2

0 2000 4000 6000 8000 10000

0 2 4 6

ln([B]0

/[B])

t / s Si mul ati on

Li near fi t

ln([D]0

/[D])

t / s

b)

Experi mental

Li near fi t

ln([D]0

/[D])

t / s a)

ln([B]0

/[B])

t / s

Figure 4.10:Simulatated (a)) and experimental (b)) results for determination ofK_Zr,1(Equation 4.16) andK_Zr,2(Equation 4.17) with the input data of 4.1.

inserted into (Equation 4.16) and (Equation 4.17). In Figure 4.9,b)and 4.10,b)the results from the experimental data are shown. Despite the higher scattering the achieved plots show good agreement with the simulated plots and the derived values are shown in Table 4.2.

Table 4.2Kinetic parameters derived from experimental NMR data of momomer-free CCG activation at 80^◦C,c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹,c(BzMgBz) = 0.044 mol L⁻¹in toluene-d₈with Equation 4.16 to 4.19.

coefficients value unit

K1,Zr 1.2 10³ mol L⁻¹ K2,Zr 8.0 10³ mol L⁻¹ kalkyl1 8.77 10⁻⁴ s⁻¹ kalkyl2 5.41 10⁻⁶ s⁻¹

High stability of the zirconium-complex magnesium-compound adductBandDare in-dicated by the equilibrium constant with values in the order of 10³mol L⁻¹to 10⁴mol L⁻¹. The individual rate coefficients are not deducible in this kind of experiment as no monomer is present. The determination of the rate coefficients is part of Section 5.1 on page 83. The reaction rate of the ligand exchange leading to alkylation within the

bimetallic complex is rather slow (see data forkalkyl in Table 4.2) which indicates that the process of yet known mechanism is energetically hardly favored. The second benzyl transfer is even slower which can be explained by larger steric constraints within the complex. After the first benzyl transfer the steric demand is higher in comparison to chloride and it reduces the possibility of a successful second exchange reaction. This result is consistent with the higher lifetime of D^P0 above the time scale of the NMR experiment indicated by the peak of the bridged benzyl species ofD^P0. The influence of this finding is discussed later for polymerization of styrene.

0 10000 20000 30000 40000

0.000 0.002 0.004

0 10000 20000 30000 40000

0.0000

0 10000 20000 30000 40000

0.000 0.005 0.010 0.015 0.020

0 10000 20000 30000 40000

0.0325

Figure 4.11:Simulated and experimental concentration vs. time profiles for monomer free CCG activation with the input data of Table4.2.

The match between simulation and experiment is improved by application of the kinetic parameters derived via pseudo-first order kinetic treatment of the NMR data in the simulation (see 4.11). For the equilibrium constants the ratio ofkex/kact was introduced into simulation by assuming the value of 1 s⁻¹forkact. The concentration vs. time profiles of B,CandD^P0 are well described by simulation while the profile of BzMgBz still is slightly drifted. For F^P0 the slope of the simulation fits excellently but the profile is minimal shifted to a lower value which may be caused by a systematic error. At low concentrations ofF^P0 the absolute concentration is determined too high because a small

13C-¹H coupling satellite from the signal ofD^P0is overlaying with the signal ofF^P0. This finding explains the high increase at low reaction times while with proceeding time the influence is lowered to a small ratio.

The shown approach was performed for further analysis of two catalyst/co-catalyst

ratios. The equilibrium constants and rate coefficients were determined at three tem-peratures (60, 70, and 80^◦C). In Figure 4.12 and 4.13 the corresponding linear plots for Zr:Mg = 1:10 are shown. For Zr:Mg = 1:20 the results are depicted in Figure 4.14 and 4.15 and the combined data of both ratios which showed no big differences as predicted by the model, is summarized in Table 4.3.

0 5000 10000 15000 20000 25000 30000 35000 40000

0 1 2 3 4 5 6

B

60 °C

70 °C

80 °C

linear fit of data

ln([B]0

/[B])

t / s

Figure 4.12: First-order rate plots of complex B for monomer-free CCG activation with Zr:Mg = 1:10. 60^◦C (blue star)c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹,c(BzMgBz) = 0.043 mol L⁻¹; 70^◦C (red triangle) c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹, c(BzMgBz) = 0.042 mol L⁻¹; 80^◦C (black square) c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹, c(BzMgBz) = 0.041 mol L⁻¹. The measurements were performed twice and the lines show the best linear fit.

Table 4.3 Kinetic parameters of momomer-free CCG activation at various temperatures and two catalyst/co-catalyst ratios, c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹, c(BzMgBz) = 0.044 mol L⁻¹; c(Cp^*₂ZrCl₂) = 0.002 3 mol L⁻¹,c(BzMgBz) = 0.046 mol L⁻¹in toluene-d₈derived by NMR data appli-cation of Equation 4.16 to 4.19.

T/^◦C K1,Zr/ 10³L mol⁻¹ K2,Zr/ 10³L mol⁻¹ kalkyl1 / 10⁻⁴s⁻¹ kalkyl2 / 10⁻⁶ s⁻¹

60 2.6±1.0 7.7±1.5 1.9±0.7

-70 2.3±0.6 8.9±2.0 5.8±2.2 3±1

80 1.2±0.2 8.8±1.2 7.8±2.2 7±3

Only for measurements with Zr:Mg ratio 1:20 at 60^◦C a kink shaped induction period is found which may be the result of the the presence of remaining diethyl ether. A detailed plot depicted in Figure 4.16 indicates two phases of reaction, a slow reaction with a rate

0 5000 10000 15000 20000 25000 30000 35000 40000 0.00

0.05 0.10 0.15 0.20 0.25

ln([D]0

/[D])

t / s D

60 °C

70 °C

80 °C

Linear fit

Figure 4.13: First-order rate plots of complex D for monomer-free CCG activation with Zr:Mg = 1:20. 60^◦C (blue star)c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹, c(BzMgBz) = 0.043 mol L⁻¹; 70^◦C (red triangle) c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹, c(BzMgBz) = 0.042 mol L⁻¹; 80^◦C (black square) c(Cp^*₂ZrCl₂) = 0.004 6 mol L⁻¹, c(BzMgBz) = 0.041 mol L⁻¹. The measurements were performed twice and the lines show the best linear fit.

0 5000 10000 15000 20000 25000

0 1 2 3 4 5 6 7

B

60 °C

70 °C

80 °C

linear fit

ln([B]0

/[B])

t / s

Figure 4.14: First-order rate plots of complex B for monomer-free CCG activation with Zr:Mg = 1:20. 60^◦C (blue star)c(Cp^*₂ZrCl₂) = 0.002 3 mol L⁻¹, c(BzMgBz) = 0.046 mol L⁻¹; 70^◦C (red triangle) c(Cp^*₂ZrCl₂) = 0.002 3 mol L⁻¹, c(BzMgBz) = 0.045 mol L⁻¹; 80^◦C (black square) c(Cp^*₂ZrCl₂) = 0.002 3 mol L⁻¹, c(BzMgBz) = 0.048 mol L⁻¹. The measurements were performed twice and the lines show the best linear fit.

0 5000 10000 15000 20000 25000 30000 35000 40000 0.00

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

D

60 °C

70 °C

80 °C

Linear fit

ln([D]0

/[D])

t / s

Figure 4.15: First-order rate plots of complex D for monomer-free CCG activation with Zr:Mg = 1:10. 60^◦C (blue star)c(Cp^*₂ZrCl₂) = 0.002 3 mol L⁻¹,c(BzMgBz) = 0.046 mol L⁻¹; 70^◦C (red triangle) c(Cp^*₂ZrCl₂) = 0.002 3 mol L⁻¹, c(BzMgBz) = 0.045 mol L⁻¹; 80^◦C (black square) c(Cp^*₂ZrCl₂) = 0.002 3 mol L⁻¹, c(BzMgBz) = 0.048 mol L⁻¹. The measurements were performed twice and the lines show the best linear fit.

0 2500 5000 7500 10000 12500 15000 17500 20000 22500 0

2 4 6

inhibition phase

second phase

linear fit inhibition phase

second phase ln([B]0

/[B])

t / s

Figure 4.16:Kink shaped inhibtion period for alkylation in monomer-free CCG activation at 60^◦C.

of 1.32(2)×10⁻⁴s⁻¹ directly followed by a fast phase with a rate of 2.8(3)×10⁻⁶s⁻¹. The value of first equilibrium constantK1,Zrshows a slight temperature dependence which can be applied to determine thermodynamic data. A plot of ln(K1,Zr) versus1/T depicted in Figure 4.17 gives a reaction enthalpy of ∆H_R = (−45±15) kJ mol⁻¹ and a reaction entropy of ∆S_R = (−69±45) J mol⁻¹K⁻¹ . The process is exotherm and entropically disfavored. For the second equilibrium constantK2,Zr, a maximum at 70^◦C appears only slight above the value of 80^◦C, i.e. that it is independent of temperature within the error tolerance.

0.00285 0.00290 0.00295 0.00300

6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6

ln(K Zr,1

/Lmol)

T 1

/ K 1

experimental

linear fit

Figure 4.17:Plot of ln(K_1,Zr) versus1/T for the determined equilibrium constant shown in Table 4.3.

Because of the low concentration of F^P0it was not possible to calculatekalkyl2for 60^◦C and therefore the investigation of temperature influences was not successful. For the rate coefficient kalkyl1 temperature dependence was found and an activation energy EA = (68 ± 23 kJ mol⁻¹) was derived from an Arrhenius plot (see Figure 4.18). The process is endotherm. Hence the alkyl-chloride exchange is energetically disfavored which indicates that the chain transfer process on the bimetallic Zr-Mg complex has a high reaction barrier. As this process is crucial for the success of the molar mass control it will strongly be influenced by temperature.

0.00280 0.00285 0.00290 0.00295 0.00300 -9.5

-9.0 -8.5 -8.0 -7.5 -7.0 -6.5 -6.0

Experimental

Linear fit

ln(kalkyl1

/s)

T 1

/ K 1

Figure 4.18:Arrhenius plot fork_alkyl1shown in Table 4.3.

Im Dokument Mechanism and Kinetics of Catalyzed Chain Growth (Seite 49-64)